Linear stability analysis of cylindrical flames
Authors:
Marc Garbey, Hans G. Kaper, Gary K. Leaf and Bernard J. Matkowsky
Journal:
Quart. Appl. Math. 47 (1989), 691-704
MSC:
Primary 80A25; Secondary 76E99
DOI:
https://doi.org/10.1090/qam/1031685
MathSciNet review:
MR1031685
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Abstract: This article is concerned with the linear stability of cylindrical flames in a velocity field generated by a line source of fuel of constant strength $2\pi \kappa$ per unit length. The mathematical model involves the equations of mass and heat transfer in the regions on either side of the flame sheet and a set of jump conditions across the flame sheet. It admits a basic solution representing a stationary flame front in the shape of a circular cylinder at a radial distance $\kappa$ from the line source. The circular front loses stability if either (i) the Lewis number of the reaction-limiting component is less than some critical value less than 1 and $\kappa$ is greater than a critical value, or (ii) the Lewis number is greater than a critical value greater than 1. In the former case the circular front evolves into a steady cellular front, in the latter into a pulsating front, which may also be cellular. The WKB method is employed to derive approximations for the pulsating and cellular branches of the neutral stability curve.
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J. D. Buckmaster and G. S. S. Ludford, Theory of Laminar Flames, Cambridge University Press, Cambridge, 1982
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G. H. Markstein, Nonsteady Flame Propagation, MacMillan, New York, 1964
G. I. Sivashinsky, Diffusional thermal theory of cellular flames, Combustion Science and Technology 15, 137–145 (1977)
B. J. Matkowsky, L. J. Putnick, and G. I. Sivashinsky, A nonlinear theory of cellular flames, SIAM J. Appl. Math. 38, 489–504 (1980)
B. J. Matkowsky and G. I. Sivashinsky, An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. Appl. Math. 37, 686–700 (1979)
J. Murray, Asymptotic Analysis, Springer-Verlag, New York, 1984
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Article copyright:
© Copyright 1989
American Mathematical Society